A frequency distribution for the response time for EMTs after a 911 call is shown below. Response Time for EMTS

Frequency

Response Time

(in minutes)

7-7.9

19

8-8.9

23

9-9.9

38

47

10 - 10.9

11 - 11.9

12 - 12.9

43

29

13-13.9

21

Step 2 of 2: Calculate the population variance for the response time. Round any intermediate calculations, if needed, to no less than four decimal places, and round

your final answer to two decimal places.

σ² = 2.90

Step-by-step explanation: For a frequency table, population variance is calculated by:

where

f is frequency

μ is expected value or mean of the distribution

In this case, mean of the distribution for a grouped frequency table is calculated by:

where

x is (as the data is grouped) the mid value of the response time

So, the table is

x          |      f

6.45    |    18

7.45    |    21

8.45    |    34

9.45    |    46

10.45   |    46

11.45    |    25

12.45   |    21

And mean will be:

μ = 9.5874

To calculate the variance, the formula above is transformed into

So, to facilitate the calculations, divide each term in a table:

    f      |      x     |      f.x       |        f.x²    

   18    |    6.45  |    116.1     |   748.845

   21    |   7.45   |  156.45   |  1165.5525

   34   |  8.45    |  287.3     | 2427.685

   46   |  9.45    | 434.7      |  4107.915

   46   | 10.45   | 480.7      |  5023.315

   25   |  11.45   | 286.25    |  3277.5625

   21    | 12.45   | 261.45     | 3255.0525

∑ 211   |             |  2022.95 |  20005.9275

Population variance will be:

= 19394.9133

σ² = 2.90

The population variance for the response time for EMTs is 2.90.

14m^2 +35

Step-by-step explanation: