Histograms DI – Medium Level – U7 – Data Interpretation – Paper 1

Medium Histogram DI needs 2-step thinking like combined ranges, ratios, and midpoint-based averages. You must read the data correctly and calculate neatly without confusion. Practice daily one Histogram DI set for 10–15 minutes, and focus on reducing calculation mistakes.

DI Set 1: Graph DI (Histogram: Daily Study Hours of Aspirants)

Data:

Study Hours Range (hours/day)	Number of Students
0–1	8
1–2	18
2–3	28
3–4	24
4–5	14
5–6	8

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xychart-beta
  title "Histogram: Daily Study Hours of Aspirants"
  x-axis ["0-1","1-2","2-3","3-4","4-5","5-6"]
  y-axis "Students" 0 --> 30
  bar [8,18,28,24,14,8]

Questions (MCQ):

Q1: How many students studied at least 3 hours per day?
A) 40;
B) 44;
C) 46;
D) 48;

Q2: What is the ratio of students in 2–3 hours range to students in 4–6 hours range (4–5 and 5–6 combined)?
A) 11:14;
B) 14:11;
C) 7:6;
D) 6:7;

Q3: What is the estimated average study time (in hours) using class midpoints?
A) 2.84;
B) 2.92;
C) 3.08;
D) 3.16;

Q4: What percentage of students studied between 1 and 4 hours (1–2, 2–3, 3–4 combined)?
A) 64%;
B) 68%;
C) 70%;
D) 72%;

Q5: What percentage of students studied less than 3 hours (0–1, 1–2, 2–3 combined)?
A) 52%;
B) 54%;
C) 56%;
D) 58%;

Answers and Explanations:

Answer (Q1): C) 46
Explanation:

“At least 3 hours” = (3–4) + (4–5) + (5–6).
24 + 14 + 8 = 46.

Answer (Q2): B) 14:11
Explanation:

2–3 hours = 28 students.
4–6 hours = 14 + 8 = 22 students.
Ratio = 28:22 = 14:11.

Answer (Q3): B) 2.92
Explanation:

Use midpoints: 0.5, 1.5, 2.5, 3.5, 4.5, 5.5.
Weighted sum = 292 and total students = 100.
Average = 292/100 = 2.92 hours.

Answer (Q4): C) 70%
Explanation:

Students from 1–4 hours = 18 + 28 + 24 = 70.
Percentage = (70/100) × 100 = 70%.

Answer (Q5): B) 54%
Explanation:

Students below 3 hours = 8 + 18 + 28 = 54.
Percentage = (54/100) × 100 = 54%.

DI Set 2: Graph DI (Histogram: Monthly Mobile Data Usage of Users)

Data:

Data Usage Range (GB/month)	Number of Users
0–5	10
5–10	22
10–15	28
15–20	20
20–25	12
25–30	8

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xychart-beta
  title "Histogram: Monthly Mobile Data Usage of Users"
  x-axis ["0-5","5-10","10-15","15-20","20-25","25-30"]
  y-axis "Users" 0 --> 30
  bar [10,22,28,20,12,8]

Questions (MCQ):

Q1: How many users used between 10 GB and 20 GB (10–15 and 15–20 combined)?
A) 44;
B) 46;
C) 48;
D) 50;

Q2: What percentage of users used more than 15 GB (15–20, 20–25, 25–30 combined)?
A) 35%;
B) 38%;
C) 40%;
D) 42%;

Q3: What is the estimated average data usage (in GB) using class midpoints?
A) 13.2;
B) 13.8;
C) 14.4;
D) 15.0;

Q4: What is the ratio of users using 5–15 GB to users using 15–30 GB?
A) 4:5;
B) 5:4;
C) 6:5;
D) 7:6;

Q5: If a bonus is given to users who used 20 GB or more, how many users get the bonus?
A) 16;
B) 18;
C) 20;
D) 22;

Answers and Explanations:

Answer (Q1): C) 48
Explanation:

10–20 GB = (10–15) + (15–20).
28 + 20 = 48.

Answer (Q2): C) 40%
Explanation:

More than 15 GB = 20 + 12 + 8 = 40 users.
Percentage = (40/100) × 100 = 40%.

Answer (Q3): B) 13.8
Explanation:

Midpoints: 2.5, 7.5, 12.5, 17.5, 22.5, 27.5.
Weighted sum = 1380 and total users = 100.
Average = 1380/100 = 13.8 GB.

Answer (Q4): B) 5:4
Explanation:

5–15 GB users = 22 + 28 = 50.
15–30 GB users = 20 + 12 + 8 = 40.
Ratio = 50:40 = 5:4.

Answer (Q5): C) 20
Explanation:

20 GB or more = (20–25) + (25–30).
12 + 8 = 20 users.

DI Set 3: Graph DI (Histogram: Delivery Time for Food Orders)

Data:

Delivery Time Range (minutes)	Number of Orders
0–10	6
10–20	14
20–30	22
30–40	18
40–50	12
50–60	8

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xychart-beta
  title "Histogram: Delivery Time for Food Orders"
  x-axis ["0-10","10-20","20-30","30-40","40-50","50-60"]
  y-axis "Orders" 0 --> 24
  bar [6,14,22,18,12,8]

Questions (MCQ):

Q1: How many orders took between 20 and 50 minutes (20–30, 30–40, 40–50 combined)?
A) 48;
B) 50;
C) 52;
D) 54;

Q2: What is the cumulative number of orders delivered within 30 minutes (0–10, 10–20, 20–30 combined)?
A) 38;
B) 40;
C) 42;
D) 44;

Q3: What is the estimated average delivery time (in minutes) using class midpoints?
A) 28;
B) 30;
C) 32;
D) 34;

Q4: What percentage of orders were delivered within 40 minutes (0–10 to 30–40 combined)?
A) 70%;
B) 72.5%;
C) 75%;
D) 77.5%;

Q5: What is the ratio of orders taking more than 30 minutes to orders taking 30 minutes or less?
A) 19:21;
B) 21:19;
C) 38:42;
D) 42:38;

Answers and Explanations:

Answer (Q1): C) 52
Explanation:

20–50 minutes = 22 + 18 + 12.
Total = 52 orders.

Answer (Q2): C) 42
Explanation:

Within 30 minutes = 6 + 14 + 22.
Total = 42 orders.

Answer (Q3): B) 30
Explanation:

Midpoints: 5, 15, 25, 35, 45, 55.
Weighted sum = 2400 and total orders = 80.
Average = 2400/80 = 30 minutes.

Answer (Q4): C) 75%
Explanation:

Within 40 minutes = 6 + 14 + 22 + 18 = 60 orders.
Percentage = (60/80) × 100 = 75%.

Answer (Q5): A) 19:21
Explanation:

More than 30 minutes = 18 + 12 + 8 = 38.
30 minutes or less = 6 + 14 + 22 = 42.
Ratio = 38:42 = 19:21.

DI Set 4: Graph DI (Histogram: Monthly Sales Units of Small Shops)

Data:

Sales Range (units/month)	Number of Shops
0–20	9
20–40	17
40–60	26
60–80	22
80–100	16
100–120	10

Graph Type: Histogram

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xychart-beta
  title "Histogram: Monthly Sales Units of Small Shops"
  x-axis ["0-20","20-40","40-60","60-80","80-100","100-120"]
  y-axis "Shops" 0 --> 28
  bar [9,17,26,22,16,10]

Questions (MCQ):

Q1: How many shops sold between 40 and 80 units (40–60 and 60–80 combined)?
A) 44;
B) 46;
C) 48;
D) 50;

Q2: What percentage of shops sold at least 60 units (60–80, 80–100, 100–120 combined)?
A) 44%;
B) 46%;
C) 48%;
D) 50%;

Q3: What is the estimated average sales (in units) using class midpoints?
A) 58.6;
B) 59.8;
C) 60.4;
D) 61.2;

Q4: By how many shops does the 20–60 range exceed the 60–100 range?
A) 3;
B) 5;
C) 7;
D) 9;

Q5: If each shop in the 100–120 range sells 15 units more next month, what is the total increase in units?
A) 120;
B) 135;
C) 150;
D) 165;

Answers and Explanations:

Answer (Q1): C) 48
Explanation:

40–80 units = 26 + 22.
Total = 48 shops.

Answer (Q2): C) 48%
Explanation:

At least 60 units = 22 + 16 + 10 = 48 shops.
Percentage = (48/100) × 100 = 48%.

Answer (Q3): B) 59.8
Explanation:

Midpoints: 10, 30, 50, 70, 90, 110.
Weighted sum = 5980 and total shops = 100.
Average = 5980/100 = 59.8 units.

Answer (Q4): B) 5
Explanation:

20–60 range = 17 + 26 = 43 shops.
60–100 range = 22 + 16 = 38 shops.
Difference = 43 − 38 = 5.

Answer (Q5): C) 150
Explanation:

Shops in 100–120 range = 10.
Total increase = 10 × 15 = 150 units.

DI Set 5: Graph DI (Histogram: Marks Distribution in Practice Test)

Data:

Marks Range (out of 50)	Number of Candidates
0–10	12
10–20	24
20–30	36
30–40	30
40–50	18

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xychart-beta
  title "Histogram: Marks Distribution in Practice Test"
  x-axis ["0-10","10-20","20-30","30-40","40-50"]
  y-axis "Candidates" 0 --> 40
  bar [12,24,36,30,18]

Questions (MCQ):

Q1: How many candidates scored between 20 and 40 marks (20–30 and 30–40 combined)?
A) 60;
B) 64;
C) 66;
D) 70;

Q2: What percentage of candidates scored 30 marks or more (30–40 and 40–50 combined)?
A) 35%;
B) 40%;
C) 45%;
D) 50%;

Q3: What is the ratio of candidates scoring 10–30 marks to candidates scoring 30–50 marks?
A) 4:5;
B) 5:4;
C) 6:5;
D) 7:6;

Q4: What is the estimated average marks (out of 50) using class midpoints?
A) 25.5;
B) 26.0;
C) 26.5;
D) 27.0;

Q5: How many more candidates scored 20–30 marks than 40–50 marks?
A) 12;
B) 15;
C) 18;
D) 21;

Answers and Explanations:

Answer (Q1): C) 66
Explanation:

20–40 marks = 36 + 30.
Total = 66 candidates.

Answer (Q2): B) 40%
Explanation:

30 or more = 30 + 18 = 48 candidates.
Percentage = (48/120) × 100 = 40%.

Answer (Q3): B) 5:4
Explanation:

10–30 = 24 + 36 = 60 candidates.
30–50 = 30 + 18 = 48 candidates.
Ratio = 60:48 = 5:4.

Answer (Q4): C) 26.5
Explanation:

Midpoints: 5, 15, 25, 35, 45.
Weighted sum = 3180 and total candidates = 120.
Average = 3180/120 = 26.5.

Answer (Q5): C) 18
Explanation:

20–30 has 36 candidates and 40–50 has 18 candidates.
Difference = 36 − 18 = 18.

This Tutorial is Related to: Average Using Midpoints, Di Mcq Practice, Di Medium Level, Exam-Level Di, Histogram Practice Set, Practice Daily Di, Ratio In Di, Ugc Net Aptitude, Ugc Net Histogram, Unit 7 Data Interpretation

Table of Contents

DI Set 1: Graph DI (Histogram: Daily Study Hours of Aspirants)

DI Set 2: Graph DI (Histogram: Monthly Mobile Data Usage of Users)

DI Set 3: Graph DI (Histogram: Delivery Time for Food Orders)

DI Set 4: Graph DI (Histogram: Monthly Sales Units of Small Shops)

DI Set 5: Graph DI (Histogram: Marks Distribution in Practice Test)