Question

A random sample of 20 women yields the given data on the number of minutes of exercise during the week of March 12 – 18.

10.0     90.6     48.5     50.4     57.4     99.6     0.0       5.0       0.0       0.0      

5.0       2.0       10.5     5.0       47.0     0.0       5.0       54.0     0.0       48.6

Compute the Mean, Median, Range, Standard Deviation and Variance for this set of data.

a) Mean

b) Median

c) Range

d) Standard Deviation

e) Variance

2.

The mean reading speed of students who complete a speed-reading course is 450 words per minute (wpm). The standard deviation is 70 wpm. Compute z-scores for the given reading speeds:

   a) 320 wpm

   b) 420 wpm

   c) 475 wpm

   d) 610 wpm

e) Would it be reasonable for the school offering the speed-reading course to advertise that students could expect to attain a reading level of at least 700 wpm upon completion of the course? Why or why not?

3.

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5000 fatal accidents. For these accidents, the mean speed was 42 miles per hour with a standard deviation of 15 miles per hour. Assuming the speeds are normally distributed, use the empirical rule to answer the following:

a) About what percent of vehicle speeds were between 42 and 72 miles per hour?

b) About what percent of vehicle speeds were in excess of 57 miles per hour?

c) About what percent of vehicle speeds were below 12 miles per hour?

d) About what percent of vehicle speeds were between 12 miles per hour and 57 miles per hour?

Answer 1

Answer)

A)

-Mean = sum of observations/number of observations

Mean = (10+90.6+48.5+50.5...)/20 = 26.93

- To fins median and range

We need to arrange the data in ascending order

0, 0, 0, 0, 0, 2, 5, 5, 5, 5, 10, 10.5, 47, 48.5, 48.6, 50.4, 54, 57.4, 90.6, 99.6

Median is the middlemost number of the arranged data

Data has 20 numbers

So, middlemost value would be in between 10th and 11th data value

That is in between 5 and 10

= 7.5

- range is = highest value - lowest value = 99.6 - 0 = 99.6

- To find variance we need to follow below steps

First subtract mean from each and every observation and then take the square then add them

= (10-26.93)^2 + (90.6-26.93)^2 + ...

= 19612.402

Now we need to divide 19612.402 by n-1, 19

Variance = 19612.402/19 = 1032.2316842105

-standard deviation = √variance = 32.1284