# Histograms and Measures of Central Tendency

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A. 100 lengths of steel bar were measured and their lengths In centimetres (cm) are given in the table labelled Item 36 on your worksheet.

i) Plot a histogram of the data provided.

ii) Calculate forthe data:

a) The arithmetic mean length. (Show all working).

b) The standard deviation from the mean. (Show all

working).

iii) Out of the 100 lengths of steel bar, approximately how many fall outside ±2 deviations from the mean? (Show all working).

B. Refer to the data, given as Item 37 on your worksheet. The data relates to examination scores for a sample of 80 BTEC (NC) students.

i) Group the data into 5 equal class widths and then produce a normal curve of distribution for the data.

ii) Calculate the standard deviation for the data and clearly show the arithmetic mean and 1 deviation around the mean on your normal curve of distribution.

C. Refer to the data given as Item 38 on your worksheet. The data given represents the marks out of 80 for 15 students In a BTEC distance learning assignment.

I) Calculate the mean median and modal marks.

ii) Two students who scored 76 and 54 respectively were later disqualified for cheating and their marks removed from the data

set. Calculate the mean, median and mode for the reduced set of marks.

iii) Compare the two sets of results arid explain in your own words what feature of the different types of average the new results illustrate. Make clear within your answer, which of the three different averages you think we should use for further

mathematical work on this data. Give reasons why.

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##### Solution Summary

Histograms, mean, median and mode, standard deviation and variance are investigated. The solution is detailed and well-presented. Diagrams are included and full working is shown.

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