Question 1
- Frequency distribution table
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Table 1
- Histogram
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Figure 1
- Measures of central tendency
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Table 2
Question 2
- The above is a sample and not a population. A population refers to the entire largest set of items that a study is interested in while a sample is a subset of a population.
- Standard deviation
- Interquartile range
Therefore the lower quartile is in 1.75th position after arranging the data in order from the smallest to the largest.
5884, 6014, 6214, 6916, 7209, 7223, 8158
1.75th position is between 5884 and 6014, thus 1st quartile = (5884 +6014)/2
Therefore the upper quartile is in 5.25th position after arranging the data in order from the smallest to the largest.
5884, 6014, 6214, 6916, 7209, 7223, 8158
5.25th position is between 7209 and 7223, thus 3rd quartile = (7209 +7223)/2
- Correlation coefficient
From excel output we have,
Table 3
It can be observed that the correlation coefficient between number of chocolate bars sold per week and weekly attendance is 0.98. This indicates that the two variables are highly correlated. This indicates that more chocolate bars are sold when more Holmes students attend classes and the converse is also true. It is therefore advisable for the manager of the supermarket to stock less chocolate when Holmes is closed during the holidays.
Question 3
- Regression equation
Where b is the slope and c is the y-intercept
Table
It is the weekly attendance that affects the number of chocolate bars sold in a week. So weekly attendance is the independent variable (x) while number of chocolate bars sold in a week is the dependent variable (y)
When Holmes is closed it means x = 0
So to calculate the number of chocolate bars sold, we have,
When students increase by 10 we have;
- Coefficient of determination
Coefficient of determination of 0.95 indicates that 95% of the variation in the dependent variable (number of chocolate bars per week) is caused by the independent variable (number of students attending Holmes in a week).
Question 4
- Holmes or receiving grass root training
P (H or GR) = P (H) + P (GR)
- External and scientific
P (E and SC) = P (E) X P (SC)
- Scientific training in Holmes
- Training is independent of from recruitment. This is because the sum of the probability of all the possible outcome is equal to
Question 5
- P (A and X)
P (A and X) = P (A) X P(X)
- P (X= first preference)
Question 6
- P (2 or less people)
- Poisson distribution
Question 7
- P (x>2,000,000)
Mean = 1,100,000
Standard deviation = 385,000
From the normal tables Z-value of 2.34 corresponds to a probability of 99.01%
Therefore P (x>2,000,000) = (100 - 99.01) = 0.99%
P (x>2,000,000) = 0.99%
- P (1,000,00 < x < 1,100,000)
P (Z=0) = 50%
P (Z= - 0.26) = 60.26%
Therefore
Question 8
You can still use the normal use the Z-distribution to test assistant’s research findings since the sample size of 50 is already greater than 30.