Statistics on social life

How many people scored 75 or lower on the questionnaire, according to the cumulative frequency polygon below?
On the exam, the students received a score of less than 75.
The populations of the world's ten most prominent countries (rounded to the nearest million inhabitants) were as follows in 2000, according to UN figures:
Indonesia
Japan
Pakistan
India
Bangladesh
Brazil
Russia
Nigeria
China
The U.S.
212129
156
1014
129
170
147
112
1278
278
Mean
The mean is calculated by multiplying the total number of countries' inhabitants by the total number of countries. The total population of the two countries is 3,625 people. 362.5 is the total amount divided by ten (the number of countries). Therefore, the mean is 362.5.

Median

The median involves arranging the numbers in an ascending or descending order and afterward finding the number that lies in the middle. The median of the data is 170.

Mode

The mode is the number that appears most in the data given. In this data, the mode is 129.

Range

The range involves subtracting the highest data from the lowest data, which in this case would be 1166.

The variance

Finding the variance involves finding the mean of the data. Subsequently, one subtracts the mean from each number and the squares the result. The variance is found using a formula. The variance of the data is 159031.65.

The standard deviation

Finding the standard deviation involves first finding the mean of the data. One should then subtract the mean from each number and then square the result. The square root of the variance is then calculated which results in the standard deviation. The standard deviation of the data is 398.7877255.

Indicate how many standard deviations a score is from the mean. Make sure to use the notation described in lecture.

Mean of 5, s of 2, a score of 1

 

The mean is subtracted from the score to get the deviation. The result is divided by the standard deviation, and this equates to the number of standard deviations the score is from the mean. The answer, in this case, is -2.



mean of 3, s of 3, a score of 9

The answer, in this case, is 2.



mean of 7, s of 10, a score of 12

The answer, in this case, is 0.5.



mean of 10, s of 20, a score of 10

The answer, in this case, is 0.



A student takes a final exam for two classes. In Class A, the average grade was a 79, with a standard deviation of 1. In Class B, the average grade was 85, with a standard deviation of 7. The student receives a grade of 81 on the exam for Class A and a grade of 90 for class B. For which exam did she do better, relative to the rest of the class? Explain why.



The student performed well in Class A than Class B and compared to the rest of the class. If the standard deviation of Class A is, one, it means that the performance range was not wide. Since the mean is 79; therefore, most of the rest of the students scored marks closer to 79 whereas this student scored 81. In Class B, the standard deviation is 7 indicating a wide range of marks where some performed so well, where others performed so poorly. In this case, the mean mark is 85. This student scored 90, which is five marks from the mean. These 5 marks are not enough to make the mean be 85, and this means some other students had higher marks than this student hence their excess marks from 85 balances those of who had poor performance.