# Use the data to solve the problems 17,19,20,21,23,23,24,30,33,40 Find the mean, median mode, lower quartile and upper quartile. Make a histogram of the data, with intervals of five.

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### 1 Answer

Let us first define the terms.

Mean is the average of the data: `(sum_(i=1)^n x_i)/n` .

Median is the numerical value that divides the data set into the upper half and lower half (when arranged in increasing order). In short, the middle value if you have an odd number of points, or the average of the two middle values if you have even.

Mode is the value that appears most often.

Quartiles divide your data set (arranged in increasing order) into four groups (hence, comprising of 25% of the data). The first quartile consists of the lowest 25% while the third quartile, the highest 25%. We can calculate the first/third quartile by getting the middle number between the lowest/highest value and the median.

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Mean: `(17+19+20+21+23+23+24+30+33+40)/10 = 250/10 = 25`

Median: `(23+23)/2 = 23` You have an even number of data points, so we pick the middle two values and get their average.

Mode: 23 (appears twice, the rest only once)

Lower Quartile: First half of data consists of 17, 19, 20, 21, 23. The median of which is 20 - Q1.

Upper Quartile: Second half of data consists of 23, 24, 30, 33, 40. The median is 30 - Q3.

Hence, the mean of the data set is 25, the median is 23, the mode is also 23, lower quartile (or first) is 20, and upper quartile (or third) is 30.

*histogram is attached

[Extra Note: You can use R-statistics software to solve for these kinds of problems and to generate nice plots. Note, however, that you should study how R works first, as it will give a different Q1 and Q3 value. The rules for computing quartiles are in the reference.

If you use R:

data = c(17,19,20,21,23,23,24,30,33,40) assigns the data set to the variable data. Then, you simply have to get the summary:

summary(data) to get all those parameters, except for the mode.

hist(data) generates the histrogram attached.]

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