STATISTICS QUESTIONS

Statistics questions



Statistics questions

Question 1

A)

Mean: The addition of a list of figures, split up by the total number of figures in the list. Also called arithmetic mean

Four tests results: 15, 18, 22, 20The sum is: 75Divide 75 by 4: 18.75

The signify' (Average) is 18.75

(Often rounded to 19)

Median: "Middle worth" of a list. The smallest number such that at smallest half the numbers in the register are no larger than it. If the register has an odd number of entries, the median is the middle application in the register after sorting the register into expanding order. If the list has an even number of applications, the median is identical to the addition of the two middle (after arranging) numbers split up by two. The median can be approximated from a histogram by finding the smallest number such that the locality under the histogram to the left of that number is 50%

Examples:

Find the Median of: 9, 3, 44, 17, 15 (Odd amount of numbers)Line up your numbers: 3, 9, 15, 17, 44 (smallest to largest)The Median is: 15 (The number in the middle)

Find the Median of: 8, 3, 44, 17, 12, 6 (Even amount of numbers)Line up your numbers: 3, 6, 8, 12, 17, 44Add the 2 middles numbers and divide by 2: 8 12 = 20 ÷ 2 = 10The Median is 10.

Mode: For lists, the mode is the most widespread (frequent) value. Alist can have more than one mode. For histograms, a mode is a relation greatest ("bump"). Afacts and figures set has no mode when all the figures appear in the data with the identical frequency. Afacts and figures set has multiple modes when two or more values emerge with the identical frequency.

Examples:

Find the mode of:9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,Put the numbers is order for ease:3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,The Mode is 15 (15 occurs the most at 3 times)

It is significant to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers.

Occasionally in Statistics you'll be inquired for the variety' in a set of numbers. The range is easily the the smallest number subtracted from the largest number in your set. Thus, if your set is 9, 3, 44, 15, 6 - The variety would be 44-3=41. Your range is 41.

Anatural progression once the 3 periods in statistics are understood is the notion of probability. Probability is the possibility of an happening happening and is usually conveyed as a fraction.

B) MEASURES OF DISTRIBUTION

Skewness, a3

If a frequency circulation is unimodal and symmetric about the signify it has a skewness of0. Values greater than 0 suggest skewness of a unimodal distribution to the right, whilst values less than 0 indicate skewness to the left, A function of the 3rd moment about the mean (denoted by a3 with a ^ symbol above ...