Good Example Of Measures Of Central Tendency Essay

Question 1

The measures of central tendency consist of the mean, median and mode and they act as an average of the entire sample. The mean of a set of numbers is calculated by summing the individual’s terms of that set and dividing by the count of the set. The median is obtained by arranging the values in ascending or descending order and obtaining the middle value. The mode represents the number that occurs most in any set of data. In the case of grouped frequencies, then the mode is represented by the group with the highest frequency.

Question 2

The mean retirement age is 66.25 and when rounded off the mean retirement age is 66 years. The stem and leaf plot is included in the appendix. The mean is calculated from the formula (∑ Xi)/ n where Xi are the individual values and n is the count.

Question 3

The mean number of car magazines sold is 28.5, the median number of car magazines sold was 26.5 and the mode number of car magazines sold was 28.the values of the mean, median and mode are obtained from (∑X)/n, (n+1)/2 and observing the most repeated value respectively
The mean is the most preferred measure of central tendency, but it is usually affected by outliers. In the case of the average car magazines sold the measure of central tendency that best represents the data is the mean, the extreme value does not impact the value of the mean since the other measures of central tendency are within reasonable range.
There are no outliers in the dataset, but there is a high extreme which is the value 62. The formula for determining an outlier is 1.5* the upper quartile value for high outliers and 1.5*the lower quartile for lower outliers.

Question 4

The average score of the tests should be 75% thus we will have to multiply this value with the total count of the scores that make up the average. 75*5= 375. In order to achieve the minimum score on the final exam, we will subtract the total of the prior four results from 375, and the value of the minimum score obtained is 70%.

Question 5

(b) The mean of the raw data is obtained to be 5.22. The mean is computed from the formula (∑fX)/ n where f is the frequency of the group and X is the midpoint of the group interval and n is the sum of the frequencies.
(c) The median of the raw data is given by 6. The median is obtained from the formula (n+1)/2 which gives the 12t value contained in the group (5-6). The cumulated frequency of the first two groups is 9 and the median is the third value in the group (5-6). The median is, therefore, computed to be 3/8* class group (1) + 5 = 5.375

Question 6

The mean of the number of inches of snow is given by 3.71, and the median is 3, the mode is obtained to be 2 which are obtained from (∑X)/n, (n+1)/2 and observing the most repeated value respectively.
The best measure of central tendency is the median since the mean is affected by a high outlier which is the value for Wednesday, which is 10.
When the value for Wednesday is removed the mean of the number of inches of snow is given by 2.67, the median is 2.5, and the mode is obtained to be 2. The values of the mean, median and mode are obtained from (∑X)/n, (n+1)/2 and observing the most repeated value respectively.
The measure of central tendency especially the mean is affected by outliers and as such its use as the representative of the dataset is questionable. In such cases, the median is usually the preferred measure of central tendency.

Question 7

The mean of the data is $21,000, and the median is $23,000. The values of the mean and median are obtained from (∑X)/n, and (n+1)/2 respectively.
The measure that best represents the measure of central tendency is the median because it is less likely for it to be affected by outliers.
The possible outlier in this data is the value $ 45,000. The outlier does not affect the mean of the data much because it has a small frequency, and the frequency of the minimum value $15,000 is much higher hence the mean remains in expected value.

Question 8

The letters in the boxplot represent the maximum value of the observation, the first quartile, the median, the third quartile, and the minimum value of the observation.

Question 9

The boxplot is included in the appendix
The five points of the boxplot are; 93, 87, 82.5, 75, and 55.

Question 10

An observation of the boxplot indicates that the median is approximately 82.5.

The range can be achieved by subtracting 55 from 93 which gives 38.

The interquartile range can be obtained by subtracting 75 from 87 which is equal to 12.
The boxplot has three divisions which separate a set of data into four equal part the divisions are the first quartile, the second quartile and the third quartile. The boxplot also indicates the minimum and maximum values of a data set. As such the boxplot is made up of five parts.

Appendix:

Stem and leaf
Boxplot