Bakery Scale-Up: Compare the Trial Batches

Compare centers, spreads, and overlap before baking for a school event.

Portion Trials

A bakery is scaling recipes for a school event. Use these trial measurements to compare two portioning methods. MAD is the mean of the absolute distances from the mean.

Muffin Batter Portions
Trial	Hand scoop (g)	Portion guide (g)
1	36	39
2	40	43
3	40	43
4	44	47

Find the mean portion mass for each method.

Hand scoop: g; portion guide: g

Calculate each method's MAD using all four measurements.

Hand scoop MAD: g; portion guide MAD: g

Measure the distance between the two means in units of their shared MAD. Divide the mean gap by the MAD.

The means are MADs apart.

Treat each method's minimum-to-maximum interval as its observed range interval. Which statement describes their overlap?

A. The intervals overlap from 39 g through 44 g.B. The intervals do not overlap because their means differ.C. The intervals overlap from 40 g through 43 g.D. The intervals overlap from 36 g through 47 g.

For a larger muffin recipe, the bakery adds exactly 5 g to every recorded portion in both methods. How does this change the distance between the means in MAD units?

A. It becomes 4 MADs because the mean gap increases.B. It becomes 0 MADs because both means increase.C. It becomes 6.5 MADs because 5 is added to the gap.D. It stays at 1.5 MADs because both sets shift equally.

Baking-Time Trials

The bakery tests a roll recipe at two batch sizes. Read the box plots in minutes. Use IQR = Q3 − Q1 as the measure of spread.

Calculate the IQR for each batch size.

Small batch: minutes; large batch: minutes

How far apart are the medians, measured in units of the shared IQR?

The medians are IQR apart.

The boxes represent the middle 50% of each distribution. Which statement correctly compares the boxes and the full observed range intervals?

A. The boxes overlap from 20 to 28 minutes; the range intervals only touch.B. The boxes overlap from 22 to 26 minutes; the range intervals do not overlap.C. The boxes touch at 24 minutes; the range intervals overlap from 22 to 26 minutes.D. The boxes do not touch; the range intervals overlap from 24 to 26 minutes.

Select every conclusion supported by the baking-time box plots.

10.

The small-batch median remains 22 minutes. A new large-batch trial will still have an IQR of 4 minutes. What large-batch median would be exactly 2 IQRs above the small-batch median?

The new median would be minutes.

Check the Event Plan

Compare the center gap with the spread, not just the gap alone. When distribution shapes are similar, a larger gap in spread units generally suggests less overlap.

11.

The bakery compares mixing times for original and scaled recipes. Within each row, both distributions have similar shapes and the same MAD. Which recipe's pair has the greatest separation in MAD units?

Mixing-Time Comparisons
Recipe	Original mean (min)	Scaled mean (min)	Shared MAD (min)
Oat bars	8	14	3
Lemon loaves	10	15	1
Corn muffins	6	12	2
Cinnamon rolls	12	20	4

A. The oat-bar pair has the greatest separation.B. The lemon-loaf pair has the greatest separation.C. The cinnamon-roll pair has the greatest separation.D. The corn-muffin pair has the greatest separation.

12.

Two scaled cookie recipes have mean portion masses of 27 g and 33 g. Their means are 3 MADs apart, and both distributions have the same MAD. Find that shared MAD.

The shared MAD is g.

13.

Two pairs of frosting trials each have a 6 g gap between their means. The narrow-spread pair has a shared MAD of 2 g. The wide-spread pair has a shared MAD of 4 g. All four distributions have similar shapes. Which judgment is best supported?

A. The narrow-spread pair should overlap less because its gap is more MADs.B. The pairs should overlap equally because their mean gaps match.C. Neither pair can overlap because both mean gaps exceed zero.D. The wide-spread pair should overlap less because its MAD is larger.

14.

Return to the muffin portion table. Nia says, “The portion-guide mean is 1.5 MADs higher, so every portion made with the guide must be heavier than every hand-scooped portion.” Explain why that conclusion is incorrect. Use two actual measurements and explain what the 1.5-MAD comparison does tell you.