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Calculate the mean, median, and mode for the following two data sets: Males: 9, 13, 14, 9, 18, 12; Females: 15, 12, 15, 13, 11, 9.

Mathematics

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Step-by-step solution

5 steps

Here are the calculations for the data provided:

Data for Males (M1M_1): 9,13,14,9,18,129, 13, 14, 9, 18, 12
Number of data points for males (n1n_1) = 6

Data for Females (M2M_2): 15,12,15,13,11,915, 12, 15, 13, 11, 9
Number of data points for females (n2n_2) = 6

Part a· 2 steps

The mean

  1. Calculate the sum of scores for each group.

    For Males:

    ∑x1=9+13+14+9+18+12=75\sum x_1 = 9 + 13 + 14 + 9 + 18 + 12 = 75

    For Females:

    ∑x2=15+12+15+13+11+9=75\sum x_2 = 15 + 12 + 15 + 13 + 11 + 9 = 75

  2. Calculate the mean for each group using the formula xˉ=∑xn\bar{x} = \frac{\sum x}{n}.

    For Males:

    xˉ1=756=12.5\bar{x}_1 = \frac{75}{6} = 12.5

    For Females:

    xˉ2=756=12.5\bar{x}_2 = \frac{75}{6} = 12.5

    The mean for males is 12.5\boxed{\text{12.5}} and for females is 12.5\boxed{\text{12.5}}.

Part b· 2 steps

The median

  1. Sort the data for each group in ascending order.

    For Males:

    9,9,12,13,14,189, 9, 12, 13, 14, 18

    For Females:

    9,11,12,13,15,159, 11, 12, 13, 15, 15

  2. Find the median.

    Since n=6n=6 (an even number) for both groups, the median is the average of the two middle values (the 3rd and 4th values).
    For Males:

    Median1=12+132=252=12.5\text{Median}_1 = \frac{12 + 13}{2} = \frac{25}{2} = 12.5

    For Females:

    Median2=12+132=252=12.5\text{Median}_2 = \frac{12 + 13}{2} = \frac{25}{2} = 12.5

    The median for males is 12.5\boxed{\text{12.5}} and for females is 12.5\boxed{\text{12.5}}.

Part c· 1 step

The mode

  1. Identify the value that appears most frequently in each data set.

    For Males:
    The data is 9,13,14,9,18,129, 13, 14, 9, 18, 12. The value 9 appears twice.
    For Females:
    The data is 15,12,15,13,11,915, 12, 15, 13, 11, 9. The value 15 appears twice.
    The mode for males is 9\boxed{\text{9}} and for females is $\boxed{\text

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