Table A below shows the price index for thirteen countries in four food categories for the year 2015 - Leaving Cert Mathematics - Question 7 - 2019

Fruits, Vegetables and Potatoes Data in Increasing Order

• 48, 62, 65, 72, 75, 91, 116, 125, 136, 150, 172

Median Calculation

The median is the middle number in an ordered list. Since there are 13 values, the median will be the 7th value:

• Median: 116

Meat Data

• 132, 117, 106, 63, 56, 54, 85, 111, 157, 54, 111, 131, 254, 78, 112

Mean Calculation

Sum of values: $132 + 117 + 106 + 63 + 56 + 54 + 85 + 111 + 157 + 54 + 111 + 131 + 254 + 78 + 112 = 1456$ Number of countries: 13

Mean = ( \frac{1456}{13} = 112 )

Standard Deviation Calculation

For the Meat category:

1. Find the mean (calculated above): 112
2. Calculate the squared differences from the mean: $\text{Variance} = \frac{(x_i - \mu)^2}{N}$ After computation, the standard deviation (S.D.):

• S.D. = 51 (rounded to the nearest whole number)

Countries Outside One Standard Deviation

Mean = 112, S.D. = 51

1. Below one standard deviation: (112 - 51 = 61)
2. Above one standard deviation: (112 + 51 = 163)

Countries not within one standard deviation:

• Macedonia (56)
• Poland (54)
• Turkey (78)

Table C

• Ireland:

  • Meat: 36.04
  • Fish: 31.32
  • Milk, Cheese and Eggs: 24.32
  • Fruits, Vegetables and Potatoes: 31.28
  • Total Cost: 122.96

• Poland:

  • Meat: 18.36
  • Fish: 18.56
  • Milk, Cheese and Eggs: 12.35
  • Fruits, Vegetables and Potatoes: 14.26
  • Total Cost: 63.53