Priya - Statistics HW 2

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East West University *

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Statistics

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Apr 3, 2024

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2.60 The number of families is eight. So, n = 8 Sum of x is. ∑x = 1+2+1+3+2+1+5+3 = 18 So mean of X will be = 18 / 8 = 2.25 Hence, the mean of   x   will be = 2.25 --------------------------------------------------------------------------------------------------------------------- 2.63 (a) The number of states is 6. So, n = 6 Let x shows the miles in each state so sum of x is, ∑x = 16+132+124+191+183+299 = 945 = 945 / 6 = 157.5 Hence, the mean number of miles in each state along I-64 is = 157.5 miles (b) I-64 intersects with nine other interstate highways, besides I-264 and I-270 at its end points so there are total 11 interchanges. Therefore number of sections is 11 so, n = 11 ∑x = 16+132+124+191+183+299 = 945 So mean of x will be = 945 / 10 = 94.5 Hence, the mean distance between interchanges with other interstate highway along I-64 is 94.5 miles ---------------------------------------------------------------------------------------------------------------------
2.67 Let us rearrange the heights in ascending order: 70, 72, 73, 74, 76 Median is the middle data value of the ordered data. So, median height of a basketball team is 3rd data value of the data set. Hence, the required median is 73 inches. --------------------------------------------------------------------------------------------------------------------- 2.71 Mode of a data set is the data value which has largest frequency. So mode of the number of cars per apartment is 2. --------------------------------------------------------------------------------------------------------------------- 2.73 (a) The number of data values is six. So, n = 6 ∑x = 9+6+7+9+10+8 = 49 So, mean of x will be = 49/6 = 8.2 Hence, the mean of x will be = 8.2 arrange the data in ascending order: 6, 7, 8, 9, 9, 10 Median is the middle data value of the ordered data. Here number of values is even. So, median is average of 3rd and 4th value. Therefore, 8+9 / 2 Hence the median is 8.5 Mode of a data set is the data value which has largest frequency. So mode of the given numbers is 9. Highest value is 10 and lowest value is 6 so the midrange will be, Mid-range = Low value + high value / 2 = 6 + 10 / 2 = 8
Hence, the midrange is 8. (b) Following is the relationship between the mean, median, mode and midrange. --------------------------------------------------------------------------------------------------------------------- 2.74 (a) Here number of data values is five. So, n = 5 Sum of X is ∑x = 2+4+7+8+9 = 30 So, mean of x will be = 30 / 5 = 6 Hence the mean of X will be 6 (b) Let us arrange the data in ascending order: 2, 4, 7, 8, 9 Median is the middle data value of the ordered data. Here number of values is odd. So, median is 3rd value. Hence, median is 7. (c) Mode of a data set is the data value which has largest frequency. But in the data set all the values comes only once. So there is no mode of the data set. (d) Highest value is 9 and lowest value is 2 so the midrange will be, midrange = low value + high value / 2 = 2 + 9 / 2 = 5.5 Hence, the midrange is 5.5. --------------------------------------------------------------------------------------------------------------------- 2.77 (a) Let us find out mean age for the 2007 NASCAR drivers. Here the number of drivers is 10. So, n = 10 ∑x = 36+26+48+28+45+21+21+38+27+32 = 322 So mean of x will be,
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