Exercises for Question Type 1: Finding the standard deviation of grouped data with frequency table - IB | RevisionDojo

Question Type 1: Finding the standard deviation of grouped data with frequency table Exercises

Written by official IB examiners

Question 1

Skill question

Estimate the population standard deviation of the data shown. Use class midpoints and round your answer to 2 decimal places.

Class interval	Frequency
10–14	5
15–19	9
20–24	6
25–29	4

[5]

Question 2

Skill question

Estimate the standard deviation of the grouped data below. Give your answer to 2 decimal places.

Score	Frequency
1–5	7
6–10	12
11–15	9
16–20	2

[4]

Question 3

Skill question

The ages of attendees at an event are grouped as below. Calculate an estimate of the standard deviation of the ages. Round your answer to 2 decimal places.

Age (years)	Frequency
30–39	4
40–49	9
50–59	12
60–69	7
70–79	3

[5]

Question 4

Skill question

The times (in seconds) to complete a task are grouped as follows. Calculate the standard deviation of the times. Round to 2 decimal places.

Time ( $t$ )	Frequency
$100 \le t < 120$	6
$120 \le t < 140$	14
$140 \le t < 160$	22
$160 \le t < 180$	18
$180 \le t < 200$	9
$200 \le t < 220$	5

[5]

Question 5

Skill question

A sample of 30 weights (in kg) is grouped as follows. Calculate the standard deviation of the weights using class midpoints. Give your answer to 2 decimal places.

Weight (kg)	Frequency
55–64	8
65–74	12
75–84	7
85–94	3

[5]

Question 6

Skill question

Find the population standard deviation for the grouped data. Round your answer to 2 decimal places.

Value	Frequency
20–24	2
25–29	7
30–34	10
35–39	1

[5]

Question 7

Skill question

Estimate the population standard deviation of the following grouped data. Round to 2 decimal places.

Class interval	Frequency
0–4	3
5–9	7
10–14	12
15–19	5
20–24	3

[4]

Question 8

Skill question

Statistics

The heights of a group of plants are shown in the following table.

Height (m)	Frequency
2.5–4.5	5
4.5–6.5	11
6.5–8.5	18
8.5–10.5	10
10.5–12.5	6

Calculate the standard deviation of the heights using midpoints. Give the answer to 2 decimal places.

[6]

Question 9

Skill question

A set of reaction times (ms) is grouped as shown. Estimate the sample standard deviation using class midpoints. Round to 2 decimal places.

Time (ms)	Frequency
200–249	3
250–299	8
300–349	12
350–399	9
400–449	3

[4]

Question 10

Skill question

A class’s test scores are grouped in the following table. The estimated mean score is $63.5625$ . Find an estimate of the standard deviation. Round to 2 decimal places.

Score	Frequency
40–49	3
50–59	$f$
60–69	12
70–79	7
80–89	2

[6]

Question 11

Skill question

A factory measures diameters (mm) of parts, grouped as follows. Estimate the population standard deviation. Round to 2 decimal places.

Diameter (mm)	Frequency
45–54	5
55–64	9
65–74	17
75–84	20
85–94	11
95–104	8

[5]

Question 12

Skill question

A company groups delivery sizes (kg) as below. Estimate the sample standard deviation using midpoints. Round your answer to 2 decimal places.

Mass (kg)	Frequency
0–10	8
10–20	14
20–40	10
40–60	6
60–100	2

[4]

Question 13

Skill question

Calculate an estimate for the standard deviation of the following grouped data. Give your answer to 2 decimal places.

Measurement	Frequency
5–15	4
15–25	10
25–35	15
35–45	8
45–55	3

[4]

Written by official IB examiners

Question 1

Skill question

Estimate the population standard deviation of the data shown. Use class midpoints and round your answer to 2 decimal places.

Class interval	Frequency
10–14	5
15–19	9
20–24	6
25–29	4

[5]

Question 2

Skill question

Estimate the standard deviation of the grouped data below. Give your answer to 2 decimal places.

Score	Frequency
1–5	7
6–10	12
11–15	9
16–20	2

[4]

Question 3

Skill question

The ages of attendees at an event are grouped as below. Calculate an estimate of the standard deviation of the ages. Round your answer to 2 decimal places.

Age (years)	Frequency
30–39	4
40–49	9
50–59	12
60–69	7
70–79	3

[5]

Question 4

Skill question

The times (in seconds) to complete a task are grouped as follows. Calculate the standard deviation of the times. Round to 2 decimal places.

Time ( $t$ )	Frequency
$100 \le t < 120$	6
$120 \le t < 140$	14
$140 \le t < 160$	22
$160 \le t < 180$	18
$180 \le t < 200$	9
$200 \le t < 220$	5

[5]

Question 5

Skill question

A sample of 30 weights (in kg) is grouped as follows. Calculate the standard deviation of the weights using class midpoints. Give your answer to 2 decimal places.

Weight (kg)	Frequency
55–64	8
65–74	12
75–84	7
85–94	3

[5]

Question 6

Skill question

Find the population standard deviation for the grouped data. Round your answer to 2 decimal places.

Value	Frequency
20–24	2
25–29	7
30–34	10
35–39	1

[5]

Question 7

Skill question

Estimate the population standard deviation of the following grouped data. Round to 2 decimal places.

Class interval	Frequency
0–4	3
5–9	7
10–14	12
15–19	5
20–24	3

[4]

Question 8

Skill question

Statistics

The heights of a group of plants are shown in the following table.

Height (m)	Frequency
2.5–4.5	5
4.5–6.5	11
6.5–8.5	18
8.5–10.5	10
10.5–12.5	6

Calculate the standard deviation of the heights using midpoints. Give the answer to 2 decimal places.

[6]

Question 9

Skill question

A set of reaction times (ms) is grouped as shown. Estimate the sample standard deviation using class midpoints. Round to 2 decimal places.

Time (ms)	Frequency
200–249	3
250–299	8
300–349	12
350–399	9
400–449	3

[4]

Question 10

Skill question

A class’s test scores are grouped in the following table. The estimated mean score is $63.5625$ . Find an estimate of the standard deviation. Round to 2 decimal places.

Score	Frequency
40–49	3
50–59	$f$
60–69	12
70–79	7
80–89	2

[6]

Question 11

Skill question

A factory measures diameters (mm) of parts, grouped as follows. Estimate the population standard deviation. Round to 2 decimal places.

Diameter (mm)	Frequency
45–54	5
55–64	9
65–74	17
75–84	20
85–94	11
95–104	8

[5]

Question 12

Skill question

A company groups delivery sizes (kg) as below. Estimate the sample standard deviation using midpoints. Round your answer to 2 decimal places.

Mass (kg)	Frequency
0–10	8
10–20	14
20–40	10
40–60	6
60–100	2

[4]

Question 13

Skill question

Calculate an estimate for the standard deviation of the following grouped data. Give your answer to 2 decimal places.

Measurement	Frequency
5–15	4
15–25	10
25–35	15
35–45	8
45–55	3

[4]