Question

broncito burritos lets customers pick the ingredients in the burritos they order. the frequency table shows how many ingredients customers ordered in their burritos in the last hour. the next customer orders a burrito with just 1 ingredient: beans. how does including this customer affect the following measures? mean median mode range increases decreases remains the same

Explanation:

Step1: Calculate original total number of customers

Sum the frequencies: $8 + 11+14 + 8+4=45$ customers.

Step2: Calculate original sum of ingredients

$(4\times8)+(5\times11)+(6\times14)+(7\times8)+(8\times4)=32 + 55+84 + 56+32 = 259$ ingredients.

Step3: Calculate original mean

Original mean $\bar{x}_1=\frac{259}{45}\approx5.76$.

Step4: Calculate new total number of customers and sum of ingredients

New number of customers is $45 + 1=46$. New sum of ingredients is $259+1 = 260$.

Step5: Calculate new mean

New mean $\bar{x}_2=\frac{260}{46}\approx5.65$. So mean decreases.

Step6: Calculate original median

There are 45 data - points. The median is the 23rd value when ordered. Cumulative frequencies: 8 (for 4 ingredients), $8 + 11=19$ (for 5 ingredients), $19+14 = 33$ (for 6 ingredients). So original median is 6.

Step7: Calculate new median

There are 46 data - points. The median is the average of the 23rd and 24th values. Cumulative frequencies with new data: 1 (for 1 ingredient), 8 (for 4 ingredients), $8 + 11=19$ (for 5 ingredients), $19+14 = 33$ (for 6 ingredients). The 23rd and 24th values are both 6, so median remains the same.

Step8: Analyze mode

The mode is the most frequent number of ingredients. Before, the mode is 6 (frequency 14). After adding a customer with 1 ingredient, the mode is still 6, so mode remains the same.

Step9: Analyze range

Original range is $8 - 4=4$. New range is $8 - 1=7$, so range increases.

Answer:

Mean: Decreases
Median: Remains the same
Mode: Remains the same
Range: Increases