Final answer:
Quartiles divide a data set into four equal parts with the first and third quartiles representing the 25th and 75th percentiles, respectively. The interquartile range (IQR) helps identify outliers, which are data points significantly lower or higher than the rest of the data set. Variance and standard deviation are measures of data spread around the mean.
Step-by-step explanation:
Understanding Quartiles, Percentiles, and Outliers
To compute the first and third quartiles, you must first arrange the data set from smallest to largest. The first quartile (Q1) corresponds to the 25th percentile, meaning that 25 percent of the data is at or below this value. The third quartile (Q3) corresponds to the 75th percentile, indicating that 75 percent of the data is at or below this value.
To identify outliers, we use the interquartile range (IQR), which is the difference between Q3 and Q1. An outlier is a value that is significantly higher or lower than most of the other values in a data set. Typically, a value is considered an outlier if it is greater than Q3 + 1.5 × IQR or less than Q1 - 1.5 × IQR.
The range is the difference between the highest and lowest values in the dataset. The interquartile range (IQR) gives us the spread of the middle 50 percent of the data. The variance and standard deviation are measures of how spread out the data is around the mean. Variance is the average of the squared differences from the mean, and standard deviation is the square root of the variance.
To determine if there are any outliers according to the given data, one would calculate the IQR and use the above formulae to set the limits for non-outlying data. One would then compare the extremes of the data against these limits.
The complete question is:meari itiedian (i) Cempute the fing and third quaries (as percentages) for theie sasa (4). Conbuta ehe iange and ioterquaveie range (as percentapea) toe these cota. rangen interquatie tirove (e) Cripolin the varance ind thindard deviation (as a perceresge) far tivelo dota. varianice zandare devention (e) Are thers any gumars in thrie data? Ttarm vie of the tabints is very liw tar al ocheol eintricts. Are there any outliers in these data? Ther ∨...silect... plow the lower limit and above the upper limit. are 0 values is 1 value values, what can we say about the percentage of students using the company's tablets in public school diatri are 2 values ean, there are some school districts where many more students are using the tablets. are 3 values is very low f C all school districts. are 4 values 3 is very high for all school districts. Relative to the mean, use of the tablets is similar for all school districts. Relative to the mean, there are some school districts where much fewer students are using the tablets. (e) Are there any outiers in these data? There below the lower limit and bove the upper limit. are 0 values (f) Based on your calculated values, what can we is 1 value ncentage of students using the company's rabiets in public school districts? Reiative to the mean, there are some 5c are 2 values e many more students are using the tablets. Use of the tablets is very low for all sche are 3 values Use of the tablets is very high for all sch. are 4 values Reiative to the mean, use of the tablets is similar for all school districts. Relative to the mean, there are some school districts where much fewer students are using the tablets. is
: