Be low is data from a random sample of 27 department stores in DC. This data sho
ID: 2923952 • Letter: B
Question
Below is data from a random sample of 27 department stores in DC. This data shows the number of thefts caught on security cameras for these stores.
Use the data shown to complete the following:
What is the level of measurement for this variable?
Determine the modal number of thefts.
Determine the mean number of thefts.
Determine the median number of thefts.
Write a few sentences describing and interpreting the results of your calculations? Is this distribution skewed? Why or why not?
x f 1 3 2 7 3 2 5 10 6 3 12 2Explanation / Answer
(a) Level of measurement for this variable: Ratio level of measurement
EXPLANATION: Ratio level of measurement in all inclusive: order and exact value between units. In particular, only in Ratio level of measurement of data, 0 is allowed. In this case, the data is the number of thefts: So, 0 theft is also measured. So, The level of measurement of data is Ratio level of measurement.
(b) modal number of thefts: 5, since maximum frequency of 10 is for x = 5
(c) mean number of thefts = 4.2593
EXPLANATION:
x f fx
1 3 3
2 7 14
3 2 6
5 10 50
6 3 18
12 2 24
--------------------------
Total 27 115
mean = 115/27 = 4.2593
(d) median number of thefts = 5
EXPLANATION:
Writing the cumulative frequencies as follows:
x F
1 3
2 3+7=10
3 10+2 = 12
5 12+10=22
6 22+3 = 25
12 25+2 =27
Median is the value of x for cumulative frequency = N/2 = 27/2 = 13.5
13.5 occurs against x = 5 because cumulative frequency = 13.5 is included in this class betwen 12 to 22.
(e) Here
mean = 4.2593
median = 5
mode = 5
We note mean, median and mode are the three measures of central tendency are almost equal. So, the distribution is symmetric distribution - normal distribution and not skewed.
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