Answer to Question #200968 in Statistics and Probability for Khomotso

Question

The 35 learners in a grade 7 class wrote an English test out of 60. The marks are as follows: 14 20 27 31 33

40 40 41 41 41

41 42 42 46 46

49 50 51 51 52

53 54 54 56 56

57 58 59 59 60

60 60 60 56 43

Use the data above to answer me following questions:

2.1 is the data discrete or continuous? Substantiate your answer.

2.2 which graph(s) will best display this type of data? Substantiate your answer.

2.3. Calculate the following:

2.3.1. The mean ( correct to three decimal place)

2.3.2. The median

2.3.3. The mean

2.4 which is the best measures of the central tendency for this- the mean or median? Explain your answer.

2.5. Calculate the following:

2.5.1 the variance ( correct to three decimal places)

2.5.1 the interquartile range.

2.6. Use the class intervals 1_< x _< 19 , 20 _< x _<29,30 _< x _< 39 , etc ,to construct a frequency table for the English test marks of the 35 learners.

Answer 1

2.1 The data is a discrete data since discrete data is information that can only take certain values. This type of data is often represented using tally charts, bar charts or pie charts. Continuous data is data that can take any value. Height, weight, temperature and length are all examples of continuous data.

2.2 The most commonly used chart type for discrete data is the column chart. Each vertical column in the chart represents one data value, with the height of the column denoting the frequency of the value.

2.3.1 Calculating the mean.

14+20+27+31+33+40+40+41+41+41+41+42+42+46+46+49+50+51+51+52+53+54+54+56+56+57+58+59+59+60+60+60+60+56+43 = 1643

1643 divided by 35= 46.9428

Correct answer is= 46.9

2.3.2. The median

14 20 27 31 33 40 40 41 41 41 41 42 42 43 46 46 49 50 51 51 52 53 54 54 56 56 56 57 58 59 59 60 60 60 60

Correct answer= 50

2.3.3. The mean

14+20+27+31+33+40+40+41+41+41+41+42+42+46+46+49+50+51+51+52+53+54+54+56+56+57+58+59+59+60+60+60+60+56+43 = 1643

1643 divided by 35= 46.9428

Correct answer = 46.9428

2.4

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.

2.5.1 The variance

How to calculate variance.

1. Find the difference from the mean for each point. Use the formula: x_i - μ
2. Square the difference from the mean for each point: (x_i - μ)²
3. Find the average of the squared differences from the mean which you found in step 2: ∑(x_i - μ)² / N . This is the population variance formula.

Correct answer =136.0929.

2.5.1 the interquartile range.

How to calculate the interquartile range.

The interquartile range is the difference between the third quartile and the first quartile in a data set, giving the middle 50%. The interquartile range is a measure of spread; it's used to build box plots, determine normal distributions and as a way to determine 

Correct answer = 15

DATA FREQUENCY FREQUENCY

14 1 0.0286

20 1 0.0286

27 1 0.0286

31 1 0.0286

33 1 0.0286

40 2 0.0571

41 4 0.1143

42 2 0.0571

43 1 0.0286

46 2 0.0571

49 1 0.0286

50 1 0.0286

51 2 0.0571

52 1 0.0286

53 1 0.0286

54 2 0.0571

56 3 0.0857

57 1 0.0286

58 1 0.0286

59 2 0.0571

60 4 0.114

Total 35 0.9995