Question

Here is your (discrete) data 193 175 192 185 220 189 209 171 200 202 215 144 233 126 82 115 294 170 133 244 172 242 239 190 175 143 204 179 118 188 219 150 95 190 243 219 233 169 101 216 210 171 209 179 130 210 197 173 365 181 183 170 191 183 185 128 234 224 224 112 180 154 110 157 235 143 117 150 202 158 193 154 281 199 172 220 125 199 190 180 207 233 130 146 First, sort the data. Second, build a GFDT for this table with a classwidth of 25. (Be sure your lower class limits are multiples of the classwidth.) Next, answer the following questions about the data set: 1. What is the first lower class limit in your GFDT (given the classwidth of 25)? 2. Express the third class as a closed interval, i.e., [ a , b ] [a,b] . 3. Give the frequency for the third class. 4. What is the (arithmetic) mean for this data (report accurate to one decimal place)? 5. Using the GFDT, what is the mode for this data set (use the appropriate definition for mode)?(take the class with the biggest frequency [175,199], and apply the following formula (Lower class limit+Upper class limit)/2 6. What is the standard deviation for this data (report accurate to two decimal places)? 7. What is the five number summary for this data set (separate numbers with a comma)? 8. What is the IQR? 9. What usual score (i.e., non-outlier) has the largest positive z-score less than z = 2 z=2 ? (Give the data value, not the z-score.) 10. Give the fences---this would suggest something other than z-scores---for the mild outliers at the maximal end of the data set; report as a closed interval, i.e., [upper mild fence, upper extreme fence].

Answer 1

Sorting

Frequency table

1)First lower class limit = 75

2)The third class closed interval is [125,150]

3) Frequency of third class = 11

4)The mean for the data is 183.0

5)The mode for the data is 189.29

6)SD for the data is 46.32

7)Five number summary is 82,151.79,184.09,210.94,365

8)IQR = Q₃ - Q₁ = 210.94- 151.79 = 59.15

9)the score that has largest possible z score less than z=2 is 276

10)upper mild fence = Q₃ +1.5(IQR) = 299.67

Upper extreme fence = Q₃ +3(IQR) = 388.39