b)
Mean = average of data
Mean =
#(7 +32 + 34 + 31 + 26 + 27 + 23 + 19 + 22 + 29 + 30 + 36 + 35 + 31)/14#
#"mean" = (382)/14#
#color(blue)("mean" = 27 2/7#
Median = middle number, we can find this from listing the numbers from lowest to greatest and finding the middle number.
#7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31#
#7, 19, 22, 23, 26, 27, 29, 30, 31, 31, 32, 34, 35, 36#
We can take 6 numbers off each side first.
#cancel(7, 19, 22, 23, 26, 27), 29, 30, cancel(31, 31, 32, 34, 35, 36)#
Because there are two medians, we find the mean of them.
#"median" = (29 + 30)/2#
#"median" = 59/2#
#color(blue)("median" = 29.5#
Mode = the number that occurs most often
We can make a tally of each number with how many times they occur in the set of numbers.
#7# - |
#19 #- |
#22 #- |
#23 #- |
#26 #- |
#27 #- |
#29 #- |
#30# - |
#31 #- ||
#32# - |
#34# - |
#35# - |
#36# - |
We can see here that above all, #31# occurs twice, when all other numbers occur once.
#color(blue)("Mode" = 31#
Range = the difference between the highest and lowest numbers.
Range = highest number - lowest number
Range = #36 - 7#
#color(blue)("Range" = 29#
c)
we can see above that out of the #14# dogs, #7# weighed less than #30# pounds. We can also say that a percentage is a number over #100#, or #x/100#
So to find the percentage, we can make this equation:
#7/14 = x/100#
Now we can find out how the first denominator gets to the next, so we can do the same to the numerator. We can make this formula to find #x#.
#(7 xx y = x)/(14 xx y = 100)#
#14 xx y = 100#
#y = 100 ÷ 14#
#y ~~ 7.147#
We can now put #7.147# in the equation in substitution for #y#
#(7 xx 7.147 = x)/(14 xx 7.147 = 100)#
Now we can find #x#.
#x = 7 xx 7.147#
#x = 50#
#x = 50%#
#therefore# #50%# of the dogs weighed less than #30# pounds.
