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Use TABLE 2 above to match the definitions with the terminology below.

Mathematics

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4 steps
  1. Sort the data set.

    The data set from the previous question, representing the amount of time spent (in minutes) by 32 customers, is:
    18, 25, 30, 15, 12, 28, 35, 22, 10, 40, 17, 20, 23, 32, 27, 19
    21, 26, 31, 16, 13, 29, 36, 24, 11, 41, 18, 21, 24, 33, 28, 20

    Sorted data (n=32):
    10, 11, 12, 13, 15, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 35, 36, 40, 41

  2. Calculate the percentage of quick shoppers (1.2.3).

    Quick shoppers are customers who spent 20 minutes or less.
    From the sorted data, the values ≤20\le 20 are: 10, 11, 12, 13, 15, 16, 17, 18, 18, 19, 20, 20.
    There are 12 quick shoppers.
    Total number of customers = 32.

    Percentage of quick shoppers=Number of quick shoppersTotal customers×100%\text{Percentage of quick shoppers} = \frac{\text{Number of quick shoppers}}{\text{Total customers}} \times 100\% Percentage of quick shoppers=1232×100%\text{Percentage of quick shoppers} = \frac{12}{32} \times 100\% Percentage of quick shoppers=0.375×100%\text{Percentage of quick shoppers} = 0.375 \times 100\% Percentage of quick shoppers=37.5%\text{Percentage of quick shoppers} = \boxed{37.5\%}
  3. Identify an outlier in the data set (1.2.4).

    To identify an outlier, we can use the 2-standard deviation rule.
    First, calculate the mean (xˉ\bar{x}) and standard deviation (σ\sigma).
    Sum of all values (∑x\sum x) = 752
    Number of values (n) = 32

    xˉ=∑xn=75232=23.5\bar{x} = \frac{\sum x}{n} = \frac{752}{32} = 23.5

    The sum of squared differences from the mean (∑(xi−xˉ)2\sum (x_i - \bar{x})^2) = 2218 (calculated in thought process).

    σ=∑(xi−xˉ)2n−1=221831≈71.548≈8.458\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} = \sqrt{\frac{2218}{31}} \approx \sqrt{71.548} \approx 8.458

    Outliers are typically values that fall outside the range of xˉ±2σ\bar{x} \pm 2\sigma.
    Lower bound = 23.5−2(8.458)=23.5−16.916=6.58423.5 - 2(8.458) = 23.5 - 16.916 = 6.584
    Upper bound = 23.5+2(8.458)=23.5+16.916=40.41623.5 + 2(8.458) = 23.5 + 16.916 = 40.416
    Any value less than 6.584 or greater than 40.416 is considered an outlier.
    Looking at the sorted data, the value 41 is greater than 40.416.
    The outlier is 41\boxed{41}.

  4. Match the definitions with the terminology (1.3).

    Using TABLE 2: TERMINOLOGY USED IN MATHEMATICAL LITERACY.

    • 1.3.1 Mode: Value or values appearing most often in a data set. This matches definition G.
    • 1.3.2 50%: The even chance probability. This matches definition F.
    • 1.3.3 Median: Middle value in an ordered data set. This matches definition A.
    • 1.3.4 Mean: Sum of all values divided by the number of values. This matches definition B.
    • 1.3.5 IQR (Interquartile Range): The spread of the middle 50% of the data. This matches definition C.
    • 1.3.6 Breakeven point: The income received from the item sold and the cost price of the item are the same. This matches definition E.

    The matches are:
    1.3.1 G\boxed{\text{G}}
    1.3.2 F\boxed{\text{F}}
    1.3.3 A\boxed{\text{A}}
    1.3.4 B\boxed{\text{B}}
    1.3.5 C\boxed{\text{C}}
    1.3.6 E\boxed{\text{E}}

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