Reading Skills. Each year the director of the reading program in a school district administers a standard test of reading skills. Then the director compares the average score for his district with the national average. Figure 2.20 was presented to the school board in the year 2013. FIGURE 2.20 Average reading scores 0 2 4 6 8 10 12 14 16 18 20 22 Average score Year 2008 2009 2010 2011 2012 2013 District average National average a. Obtain a truncated version of Fig. 2.20 by sliding a piece of paper over the bottom of the graph so that the bars start at 16. b. Repeat part (a), but have the bars start at 18. c. What misleading impression about the year 2013 scores is given by the truncated graphs obtained in parts (a) and (b)?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
2.165 Reading Skills. Each year the director of the reading program
in a school district administers a standard test of reading skills. Then
the director compares the average score for his district with the national average. Figure 2.20 was presented to the school board in the
year 2013.
FIGURE 2.20
Average reading scores
0
2
4
6
8
10
12
14
16
18
20
22
Average score
Year
2008 2009 2010 2011 2012 2013
District average National average
a. Obtain a truncated version of Fig. 2.20 by sliding a piece of paper
over the bottom of the graph so that the bars start at 16.
b. Repeat part (a), but have the bars start at 18.
c. What misleading impression about the year 2013 scores is given
by the truncated graphs obtained in parts (a) and (b)?
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