Question

1. Define variability.

2. What are the strengths and limitations of the range?

3. When computing a standard deviation, why are the deviations from the mean squared?

4. Why is the square root taken when computing the standard deviation?

5. What are the three measures of variability? Which is the most commonly used?

6. Compute the range of the following student’s test scores: 39, 64.5, 54, 49, 56, 61, 58

7. The local B League baseball team is trying out new pitchers. The new pitcher will be selected based on the mean velocity of his best pitches, but also based on the standard deviation of his pitches.   Compute the standard deviation and variance for Pitcher A if S(X-M)2 = 128, for 33 attempts (n). See formula - p.49

8. A school psychologist is interested in the variability of student IQ scores. What is the standard deviation of the following IQ scores? The scores are 100, 115, 85, 125, 75, 95, 105.

9. Here is a set of cognitive ability scores: 103, 112, 97, 126, 100, 131. Comprehensively assess variability (range, standard deviation and variance).

10. The length of time it takes to fly from one place to another varies based on many factors. Given the following flight lengths, compute the average flight time, the range and the standard deviation in flight lengths. The flight lengths from Kansas City to Los Angeles are: 1 hr 40 min, 1 hr 45 min, 3 hr, 3 hr 35 min, 3 hr 20 min, 1 hr 45 min, 3 hr 15 min, 3 hr 25 min. Change all flight times to minutes.

11. Here is a set of adaptive functioning scores: 97, 122, 105, 140, 94, 129. Assess variability (range, standard deviation and variance).

12. Using the procedure explained on page 4383 of your text to find the range, variance and standard deviation of prej from chapter 2 data set 1 using SPSS.

Answer 1

(1) Variability, also called Spread or Dispersion is defined as the quatity how much spread out a set of data is. Variability gives us a way to describe how much data sets vary and allows us to use statistics to compare our data with other sets of data.

(2)

(a) Strengths of Range:

(i) Range is the simplest measure of dispersion and is calculated by subtracting the lowest score in the data set from the largest.

(ii) Range takes into consideration extreme score

(b) Limitations of Range:
(i) Range uses only two scores in the data set and ignores the rest.

(ii) The extreme scores distort the Range

(3)

When computing the a standard deviation, the deviations from the mean are squred due to the following reasons:

(i) Squaring makes each term positive so that the values above the mean do not cancel values below the mean.

(ii) Squaring adds more weighting to the larger differences, and in many cases, this extra weighting is appropriate since points further from the mean may be more significant.

(iii) The mathematics are relatively manageable when using this measure in subsequent statistical calculations.

(4)

The squareroot is taken when computing the standard deviation for the following reason:

Because the differences are squared, the units of Variance are not the same as the units of the data. Therefore, the Standard Deviation is reported as the squareroot of the Variance and the units then correspond to those of the data set.

AS PER THE DIRECTIONS FOR ANSWERING, ONLY FIRST 4 QUESTIONS ARE ANSWERED.