Deck 4: Central Tendency

Question 1

For each of the following sets of scores, find (1) the mode, (2) the median, and (3) the mean:
(a)12, 10, 8, 19, 8,
(b)14, 12, 17, 23,
(c)11, 6, 10, 11, 11, 11.

Answer 1

(a)
(b) no mode,
(c)

Question 2

(a) For the sample of scores: 7, 3, 5, 3, 3, show that . 
(b) State what means in words. To what property of the mean is it related?

Answer 2

(a)

 
(b) the sum of the deviations around the mean equals 0; the mean as the point of balance.

Question 3

What shape would you predict for each of the following distributions:
(a)
(b) (c)

Answer 3

(a)negatively skewed
(b)positively skewed
(c)symmetric.

Question 4

Which measure of central tendency would you use with the following distribution of scores? Explain.

Question 5

Professor Jones gives a quiz in her statistics course and obtains the following 20 scores:

Calculate:
(a) the mode
(b) the median
(c) the mean

Question 6

Fifty students take a quiz on which it is possible to earn a score ranging from 0 to 10. Each student writes his or her score on a slip of paper and the slips are then put in a hat and one drawn at random. We will "win" if we guess correctly the score written on the slip. We should guess

A) the mean
B) the median
C) the mode
D) a score of 5

Question 7

The median is

A) the score falling halfway between the lowest and highest scores in the distribution
B) the score point below which half of the cases fall
C) either (a) or (b) above; they mean the same thing
D) neither (a) nor (b) above

Question 8

X₈ refers to

A) a score of 8
B) a score 8th in magnitude among those in the distribution
C) the 8th score in the distribution but not necessarily the 8th in magnitude
D) the fact that there are just 8 scores in the distribution

Question 9

In the series of scores: 4, 4, 5, 7, the number 5 is

A) the mean
B) the mode
C) the median
D) none of the above

Question 10

In the series of scores: 4, 4, 5, 7, the number 4.5 is

A) the mean
B) the mode
C) the median
D) none of the above

Question 11

In the series of scores: 4, 4, 5, 7, the number 4 is

A) the mean
B) the mode
C) the median
D) none of the above

Question 12

The median of the following sample of scores: 2, 6, 3, 8, 3, 8 is

A) 5.5
B) 4.5
C) 4
D) 5

Question 13

The highest point of a frequency curve is most closely associated with

A) the mean
B) the median
C) the mode
D) P₅₀

Question 14

The mode is the most appropriate measure for

A) skewed distributions
B) flat distributions
C) discrete data
D) qualitative data

Question 15

The measure of central tendency that may be considered as the "balance point" of the distribution is the

A) mean
B) median
C) mode
D) none of the above

Question 16

If one score in a distribution is changed to another value, it is certain that, according to raw score calculation,

A) the mean has changed
B) the median has changed
C) the mode has changed
D) all these measures have changed

Question 17

If scores are expressed in terms of the amount by which they deviate from a measure of central tendency, the sum of the negative deviations will exactly equal the sum of the positive deviations when deviations are taken about

A) the median
B) the mean
C) the mode
D) any of the above measures

Question 18

Several situations tend to make the median a more attractive choice than it might otherwise be. Which, among those described below, does not add to its attractiveness?

A) the distribution is open-ended
B) the distribution is skewed
C) a measure is wanted which reflects the total of the scores
D) there are several scores which lie substantially to one side of the bulk of the scores

Question 19

Measures of central tendency differ in their resistance to the effect of sampling fluctuation. From most resistant to least resistant, the order is

A) median, mean, mode
B) mean, mode, median
C) mode, mean, median
D) mean, median, mode

Question 20

In constructing a frequency distribution, a score belonging in the top class interval is inadvertently omitted. Which measure(s) might not be affected?

A) mean
B) median
C) mode
D) median and mode

Question 21

The deviations about the mean for four out of a sample of five scores are: -3, +2, +6, -1. The fifth deviation must be

A) -4
B) +3
C) -2
D) +5

Question 22

If the mean is 130 and the median is 140, it seems likely that the

A) mode will fall in between
B) distribution is bimodal
C) distribution is positively skewed
D) distribution is negatively skewed

Question 23

The mean of a distribution of scores for a very easy test is 24.3. Which of the following is most likely to be the median?

A) 24.3
B) 21.3
C) 26.2
D) 23.6

Question 24

The mean of a distribution is 75 and the median is 72. If 20 points are subtracted from each score, the mean of this altered distribution will be

A) 75
B) 65
C) 55
D) altered in some way, but there is insufficient information to say exactly how

Question 25

For a symmetrical distribution of 10 scores the mean is calculated to be 32.6. Later it is learned that John's recorded score of 28 really should be a 35. Correcting this error will change the calculated value of

A) the mean only
B) the mean and the mode
C) the median and the mode
D) the mean and the median