Question

An advertisement for a​ speed-reading course claimed that the​ "average" reading speed for people completing the course was 1000 words per minute. Shown below are the actual data for the reading speeds per minute for a sample of 24 people who completed the course. Complete parts​ (a) through​ (c) below.

1000	900	600	1000	900	850
650	1000	1050	800	1000	850
700	750	650	950	700	1050
600	1100	950	1100	750	650

a. Find the​ mean, median,​ mode, and midrange.

What is the​ mean? Choose the correct answer​ below, and, if necessary fill in the answer box to complete your choice.

A.The mean is

nothing.

​(Round to the nearest whole number as​ needed.)

B.

There is no mean.

What is the​ median? Choose the correct answer​ below, and, if necessary fill in the answer box to complete your choice.

A.The median is

nothing.

​(Round to the nearest whole number as​ needed.)

B.

There is no median.

What is the​ mode? Choose the correct answer​ below, and, if necessary fill in the answer box to complete your choice.

A.The mode is

nothing.

​(Round to the nearest whole number as​ needed.)

B.

There is no mode.

What is the​ midrange? Choose the correct answer​ below, and, if necessary fill in the answer box to complete your choice.

A.The midrange is

nothing.

​(Round to the nearest whole number as​ needed.)

B.

There is no midrange.

b. What measure of central tendency was given in the​ advertisement?

A.

Median

B.

Mean

C.

Mode

D.

Midrange

c. Which measure of central tendency is the best indicator of the​ "average" reading speed in this​ situation? Explain your answer.

A.

Either the mode or midrange would be good measures of central tendency to use because there are no outliers.

B.

The midrange would be the best measure of central tendency to use because it is most often associated with the word​ "average".

C.

Either the mean or the median would be good measures of central tendency to use because there are no outliers.

D.

The mode would be the best measure of central tendency to use because it is the value of the speed that most people achieved.

Answer 1

Data in sorted order

600 600 650 650 650 700 700 750 750 800 850 850 900 900 950 950 1000 1000 1000 1000 1050 1050 1100 1100

a)

Mean = sum of observations / number of observations

= 20550/24 = 856.25

b)

In our case we have 24 (even) observation. so, the median is equal to the average of n/2th = 12 th and n/2 + 1 th = 13 th observation in the sorted sequence. So, 12th is 850 and 13th is 900.

So, median = (850 + 900)/2 = 875

c)

The mode is that observation which occurs most of the time

So, Mode = 1000 because it occurs most of the time.

d)

Midrange = (max + min) / 2

= (600 + 1100)/ 2 = 850

e) What measure of central tendency was given in the advertisement?

in the advertisement, the value was 1000 which is equal to mode. So, mode was given in the advertisement.

f)

D.

The mode would be the best measure of central tendency to use because it is the value of the speed that most people achieved.