# FIND STANDARD DEVIATION WITH FREQUENCY IS GIVEN WORKSHEET

Problem 1 :

Find the standard deviation of the distribution :

 Score12345 Frequency12421

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)5060708090100 Frequency139642

Solution

Problem 3 :

Find the standard deviation of the following test results.

 Test score101112131415 Frequency467232

Solution

Problem 4 :

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

 Number of chocolates2526272829303132 Frequency15713121282

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)30323436384042 Frequency11371152

Solution

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 - 369.99370 - 379.99380 - 389.99390 - 399.99400 - 409.99410 - 419.99420 - 429.99430 - 439.99 Number of Workers516271612842

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 - 79.9980 - 89.9990 - 99.99100 - 109.99110 - 119.99120 - 129.99130 - 139.99140 - 149.99 No. of families273248253721187

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.

Solution

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

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