Question

Fifteen seventh graders were randomly selected to see how many pushups in a row they could do. Their data are shown. A. b. 45, 40, 36, 38, 42, 48, 40, 40, 70, 45, 42, 43, 48, 36

Answer 1

Answer:

Mean of this data set is 43.7857

the median of this data set is 42

Step-by-step explanation:

The complete question is:

Fifteen seventh graders were randomly selected to see how many pushups in a row they could do. Their data are shown. A. b. 45, 40, 36, 38, 42, 48, 40, 40, 70, 45, 42, 43, 48, 36

a. Determine the mean of this data set.

b. Determine the median of this data set.

Given:

Data:

45, 40, 36, 38, 42, 48, 40, 40, 70, 45, 42, 43, 48, 36

To find:

a) Mean

b) Median

Solution:

a)

The formula to find Mean is :

Mean = Sum of all the values / Total number of values

          = ∑ x / n

Here there are total 14 values so n = 14

Now lets find sum of all the values

∑ x =  45 + 40 + 36 + 38 + 42 + 48 + 40 + 40 + 70 + 45 + 42 + 43 + 48 + 36

     = 613

Now compute Mean:

Mean = ∑ x / n

          =  613 / 14

         = 43.785714

Mean = 43.7857

b)

The formula to find Median is:

Since there are 14 values in the data this means the data has even number of values. So to compute the median of even number of values:

First put the values in order.

Second, find the middle pair of values in data

Third, find the value that is half way between them i.e. by adding the two middle pair values and dividing the result by 2

45, 40, 36, 38, 42, 48, 40, 40, 70, 45, 42, 43, 48, 36

Ordering the values :

36, 36, 38, 40, 40, 40, 42, 42, 43, 45, 45, 48, 48, 70

Find the middle two numbers:

42, 42

We can see that both are same values so median value is 42 but to follow the above steps:

Now add these two numbers and divide the sum by 2:

42 + 42 = 84

84/2 = 42

So the median of this data set is 42