FIND STANDARD DEVIATION WITH FREQUENCY IS GIVEN WORKSHEET

Problem 1 :

Find the standard deviation of the distribution :

Score

1

2

3

4

5

Frequency

1

2

4

2

1

Solution

Problem 2 :

The weights (in kilograms) of 25 calves were measured and the results placed in a table as shown alongside.

a. Find an estimate of the standard deviation by using interval midpoints.

Weight (kg)

50

60

70

80

90

100

Frequency

1

3

9

6

4

2

Solution

Problem 3 :

Find the standard deviation of the following test results.

Test score

10

11

12

13

14

15

Frequency

4

6

7

2

3

2

Solution

Problem 4 :

The number of chocolates in 60 boxes was counted and the results tabulated.

Number of chocolates

25

26

27

28

29

30

31

32

Frequency

1

5

7

13

12

12

8

2

Find the mean and standard deviation of the distribution.

Solution

Problem 5 :

The lengths of 30 trout were measured to the nearest cm and the following data obtained :

Find estimates of the mean length and the standard deviation of the lengths.

Length (cm)

30

32

34

36

38

40

42

Frequency

1

1

3

7

11

5

2

Solution

Answer Key

1) Mean = 3 and standard deviation = 1.10

2)  Mean = 76 and standard deviation = 16.95

3)  Mean = 12 and standard deviation = 1.5

4) Mean = 28.8 and standard deviation = 1.67

5) Mean = 37.26 and standard deviation = 2.65

Problem 1 :

The weekly wages (in dollars) of 90 workers in a steel yard are given alongside :

Find estimates of the mean wage and the standard deviation of the wages.

Wage ($)

360 - 369.99

370 - 379.99

380 - 389.99

390 - 399.99

400 - 409.99

410 - 419.99

420 - 429.99

430 - 439.99

Number of Workers

5

16

27

16

12

8

4

2

Solution

Problem 2 :

A random sample of the weekly supermarket bills for a number of families was observed and recorded in the table given.

a. Find the mean bill and the standard deviation of the bills.

b. variance of the population

Bill ($)

70 - 79.99

80 - 89.99

90 - 99.99

100 - 109.99

110 - 119.99

120 - 129.99

130 - 139.99

140 - 149.99

No. of families

27

32

48

25

37

21

18

7

Solution

Problem 3 :

The length of 30 randomly selected 12 day old babies were measured to the nearest cm and the following data obtained.

i) Find the mean length and standard deviation of the lengths.

ii) Find the variance.

standard-deviation-with-intervals-q3.png

Solution

Answer Key

1)  Mean wages = 392.10, Standard deviation = 16.34

2) Mean = 103.50, Standard deviation = 19.14

b)  Variance = 366.33

3)  i) Mean = 47.76, standard deviation = 2.65

ii) Variance = 7.05

Recent Articles

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More