Statistics questions | form six Pure Advanced Mathematics

1. The sum of 20 numbers is 320 and the sum of the squares of these numbers is 5840.

1. Calculate the mean and standard deviation of 20 numbers.
2. If one number is added to the 20 numbers so that the ean is unchanged, find this number and show whether the standard deviation will change or not.

2. A watchman at Mlimani city shopping centre recorded the length of time to the nearest minute that a sample of 131 cars was parked in their car park. The results were as follow:

1. Calculate the median time correct to four significant figures
2. By using the coding method and the assumed mean A=19.5, calculate the mean in two decimal places.

The following frequency distribution table represents a certain class of 100 students:

1. Determine the value of t.

2. Find the following measures of central tendency and dispersion correct to two decimal places:

1. Mean
2. Standard devication,
3. Mean deviation,
4. Median,

The following table shows distribution of marks in a matriculation examination of communication skills:

1. Given that the assumed mean is 75.5, use the coding method to find the average marks.
2. Determine the lower quartile of the distribution.
3. Calculate the 75^th percentile correct to four significant figures.

The masses of a sample of new potatoes were measured to the nearest gram and are summarized in the following table:

Determine the following measures of dispersion correct to three decimal places:

1. first and third quartiles.
2. semi-interquartile range.
3. seventh decile.
4. 80^th percentile.
5. variance and standard deviation.